To find the vertex of a parabola, use the quadratic formula in the standard form of y = ax^2 + bx + c, and derive the x-value of the vertex from the formula -(b/2a). Then, substitute the value of x into the equation to solve for y.
- Write the quadratic equation in standard form
The standard form of a quadratic equation is y = ax^2 + bx + c. If necessary, convert the equation into this form by moving terms around. As an example equation, use y = 3x^2 - 6x + 9.
- Find the x-value of the vertex
By using the formula -(b/2a), it's possible to derive the x-value of the vertex. In the example equation, the terms b and a are -6 and 3. Plugging these values into the formula yields -(-6)/2(3), which converts to 1.
- Substitute the x term in the original equation to derive the y-value
In the original equation of y = 3x^2 - 6x + 9, the equation is y = 3(1)^2 - 6(1) + 9, or y = 3 - 6 + 9. Simplified, this yields the vertex to be (1, 6).
- Check your work
Both sides of the equation should now be equal.